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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
180.1.f.a 180.f 20.d $2$ $0.090$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{15}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots\)
180.1.m.a 180.m 60.l $4$ $0.090$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots\)
180.1.p.a 180.p 180.p $2$ $0.090$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.1.p.b 180.p 180.p $2$ $0.090$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
180.2.a.a 180.a 1.a $1$ $1.437$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{13}+6q^{17}-4q^{19}+\cdots\)
180.2.d.a 180.d 5.b $2$ $1.437$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{5}+2iq^{7}+4q^{11}-2iq^{17}+\cdots\)
180.2.e.a 180.e 12.b $8$ $1.437$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{4}-\beta _{5}+\beta _{7})q^{4}+\cdots\)
180.2.h.a 180.h 60.h $4$ $1.437$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{8}^{3}q^{2}+2q^{4}-\zeta_{8}^{2}q^{5}+2\zeta_{8}^{3}q^{8}+\cdots\)
180.2.h.b 180.h 60.h $8$ $1.437$ 8.0.3317760000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{3}q^{4}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
180.2.i.a 180.i 9.c $2$ $1.437$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
180.2.i.b 180.i 9.c $6$ $1.437$ 6.0.954288.1 None None \(0\) \(-1\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+(\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
180.2.j.a 180.j 15.e $4$ $1.437$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2-2\zeta_{8}^{2})q^{7}+\cdots\)
180.2.k.a 180.k 20.e $2$ $1.437$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(1-2i)q^{5}+\cdots\)
180.2.k.b 180.k 20.e $2$ $1.437$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(-1+2i)q^{5}+\cdots\)
180.2.k.c 180.k 20.e $2$ $1.437$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(2-i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
180.2.k.d 180.k 20.e $8$ $1.437$ 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{2}+\beta _{4})q^{2}+(\beta _{3}+\beta _{5})q^{4}+(2\beta _{4}+\cdots)q^{5}+\cdots\)
180.2.k.e 180.k 20.e $12$ $1.437$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)
180.2.n.a 180.n 180.n $4$ $1.437$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
180.2.n.b 180.n 180.n $4$ $1.437$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(6\) \(6\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(2+\cdots)q^{5}+\cdots\)
180.2.n.c 180.n 180.n $8$ $1.437$ 8.0.3317760000.8 \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{5}q^{2}+\beta _{1}q^{3}+2\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots\)
180.2.n.d 180.n 180.n $48$ $1.437$ None None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$
180.2.q.a 180.q 36.h $48$ $1.437$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
180.2.r.a 180.r 45.j $12$ $1.437$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+(-\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)
180.2.w.a 180.w 45.l $24$ $1.437$ None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
180.2.x.a 180.x 180.x $128$ $1.437$ None None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{12}]$
180.3.b.a 180.b 15.d $4$ $4.905$ \(\Q(\sqrt{-2}, \sqrt{23})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{3})q^{5}-\beta _{2}q^{7}+7\beta _{1}q^{11}+\cdots\)
180.3.c.a 180.c 4.b $4$ $4.905$ \(\Q(\zeta_{10})\) None None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{10}q^{2}+(-1+\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{4}+\cdots\)
180.3.c.b 180.c 4.b $8$ $4.905$ 8.0.85100625.1 None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\beta _{3}q^{5}+\cdots\)
180.3.c.c 180.c 4.b $8$ $4.905$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{4})q^{4}+\beta _{3}q^{5}+2\beta _{6}q^{7}+\cdots\)
180.3.f.a 180.f 20.d $1$ $4.905$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(-2\) \(0\) \(5\) \(4\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+5q^{5}+4q^{7}-8q^{8}+\cdots\)
180.3.f.b 180.f 20.d $1$ $4.905$ \(\Q\) \(\Q(\sqrt{-5}) \) None \(2\) \(0\) \(5\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+5q^{5}-4q^{7}+8q^{8}+\cdots\)
180.3.f.c 180.f 20.d $2$ $4.905$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{2}-4q^{4}+(-3-2i)q^{5}-4iq^{8}+\cdots\)
180.3.f.d 180.f 20.d $4$ $4.905$ \(\Q(\sqrt{-3}, \sqrt{22})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.e 180.f 20.d $4$ $4.905$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(2+2\zeta_{12}^{2})q^{4}+\cdots\)
180.3.f.f 180.f 20.d $4$ $4.905$ \(\Q(i, \sqrt{15})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+5\beta _{2}q^{5}+(3\beta _{1}+\cdots)q^{8}+\cdots\)
180.3.f.g 180.f 20.d $4$ $4.905$ \(\Q(\sqrt{-3}, \sqrt{22})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.h 180.f 20.d $8$ $4.905$ 8.0.\(\cdots\).4 None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.g.a 180.g 3.b $4$ $4.905$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-4-\beta _{3})q^{7}+(-\beta _{1}-6\beta _{2}+\cdots)q^{11}+\cdots\)
180.3.l.a 180.l 5.c $2$ $4.905$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(3-4i)q^{5}+(-7-7i)q^{7}-10q^{11}+\cdots\)
180.3.l.b 180.l 5.c $4$ $4.905$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-12\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-3-2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(5+2\beta _{1}+\cdots)q^{7}+\cdots\)
180.3.l.c 180.l 5.c $4$ $4.905$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(3\beta _{2}-\beta _{3})q^{11}+\cdots\)
180.3.m.a 180.m 60.l $4$ $4.905$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}+3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.b 180.m 60.l $4$ $4.905$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(4\zeta_{8}-3\zeta_{8}^{3})q^{5}+\cdots\)
180.3.m.c 180.m 60.l $40$ $4.905$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
180.3.o.a 180.o 9.d $4$ $4.905$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None None \(0\) \(-6\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-3+3\beta _{2})q^{3}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
180.3.o.b 180.o 9.d $12$ $4.905$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{3}+\beta _{8}q^{5}+(\beta _{1}+\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
180.3.p.a 180.p 180.p $4$ $4.905$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(-4\) \(4\) \(10\) \(4\) $\mathrm{U}(1)[D_{6}]$ \(q+(-2+2\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
180.3.p.b 180.p 180.p $4$ $4.905$ \(\Q(\sqrt{-3}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(4\) \(-4\) \(10\) \(-4\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-2\beta _{2})q^{2}+(\beta _{1}-2\beta _{2}-\beta _{3})q^{3}+\cdots\)
180.3.p.c 180.p 180.p $128$ $4.905$ None None \(0\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{6}]$
180.3.s.a 180.s 36.f $96$ $4.905$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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